ANSWERS TO THE TESTS AND COMMENTS:

I'm too busy to explain all the solutions, but the answers are below.

1) A
2) A
3) 9pi
4) e
5) To be nice, I'll give credit for anything between 26% and 32%.

6) 10 - 10/sqrt3

It seems like a lot of people struggled with this one.

Here's a hint: In the drawing you know that "10(sqrt2)" is the hypotenuse of the 45 x 45 x 90 triangle CDA. Just divide by sqrt2 in order to find the two equal length sides of triangle CDA.

You also know that triangle CDB is a 30 x 60 x 90 triangle.

Remember, 30 x 60 x 90 triangles have sides x, x(sqrt3), and 2x.

45 x 45 x 90 triangles have sides x, x and x(sqrt2)

From here it should be very easy.

7) 8.6

8) c

9) d

10) b

11) b

12) a

13) a

14) b

15) c

16) e

17) d

18) .000002

You have to remember that everytime you see % you have to move the decimal over 2 places. That's why this problem fools a lot of people.

19) a

20) c

21) b

22) d

23) 10/3 or 3.33

24) This is an extremely tricky problem and harder than anything you will see on the GRE. It is the hardest problem on this test. You need to have fantastic intuition into math and recognize that the answer will be VERY close to x = 30. This might be a good problem for genius level ability. This problem difficulty is most certainly well above the 800 level on the GRE general test (given that calculators were not allowed). I didn't even provide you with answer choices to help you reason it out.

Stating that the answer will be VERY SLIGHTLY greater than 30 would have been perfectly acceptable. Even a genius isn't necessarily expected to do ridiculously difficult mental math. You can use the below equation calculator to see the exact results. x = 30.0009

QuickMath Automatic Math Solutions

25) 50
26) B
27) -1/8
28) 48 or 2 x 4!